The function performs the imputation step of the stochastic EM algorithm for the DNA model when the design is not nested. The function generates pseudo outputs \(\widetilde{\mathbf{y}}_l\) at pseudo inputs \(\widetilde{\mathcal{X}}_l\).
imputer_DNA(XX, yy, kernel=kernel, t, pred1, fit2)An updated yy list containing:
y_star: An updated pseudo-complete outputs \(\mathbf{y}^*_l\).
y_list: An original outputs \(\mathbf{y}_l\).
y_tilde: A newly imputed pseudo outputs \(\widetilde{\mathbf{y}}_l\).
A list of design sets for all fidelity levels, containing X_star, X_list, and X_tilde.
A list of current observed and pseudo-responses, containing y_star, y_list, and y_tilde.
A character specifying the kernel type to be used. Choices are "sqex"(squared exponential), "matern1.5", or "matern2.5".
A vector of tuning parameters for each fidelity level.
Predictive results for the lowest fidelity level \(f_1\). It should include cov obtained by setting cov.out=TRUE.
A fitted model object for higher fidelity levels \(f\) from \((t_{-1}, X_{-1}, y_{-1})\).
For non-nested designs, pseudo-input locations \(\widetilde{\mathcal{X}}_l\)
are constructed using the internal makenested function.
The imputer_DNA function then imputes the corresponding pseudo outputs
\(\widetilde{\mathbf{y}}_l = f_l(\widetilde{\mathcal{X}}_l)\)
by drawing samples from the conditional normal distribution,
given fixed parameter estimates and previous-level outputs \(Y_{-L}^{*(m-1)}\),
at the \(m\)-th iteration of the EM algorithm.
For further details, see Heo, Boutelet, and Sung (2025+, <arXiv:2506.08328>).